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1.04 Using technology for operations with whole numbers

Lesson

Operations with whole numbers with technology

Technology can make doing mathematical operations quicker and easier, but there are some common mistakes and pitfalls to keep in mind.

The most common type of technology used for performing operations is the hand-held calculator, so let's run through the basics.

The buttons we will use at the moment are:

An image showing calculator buttons commonly used for operations. Ask your teacher for more information.

To perform an operation between two numbers with your calculator,

  • Press the buttons corresponding to the digits of the first number going from left to right
  • Press the corresponding operation button
  • Enter the second number the same way as the first
  • Press the equals sign

The answer should now appear on the calculator display.

To evaluate an expression involving more than one operation we need to pay attention to the  order of operations  . We always evaluate inside parentheses first and, working from left to right, do any multiplication or division before addition or subtraction. If you enter the expression exactly as it appears in the question, your calculator will automatically do the correct order of operations.

Sometimes it may be quicker to break up the expression and do each operation separately. To do this, perform each operation then press the " = " button, respecting the order of operations. The answer each time you press equals becomes the 'first number' that you can then perform further operations on.

It's always useful to  check the reasonableness  of your answer. If the answer doesn't seem right, there's a good chance it isn't.

There are many mistakes that can occur when using your calculator, here are some common ones:

  • Not using the correct order of operations

  • Missing a digit from a number

  • Swapping the digits in a number

  • Swapping numbers in the expression

  • Using the wrong operation

  • Adding an extra digit

Calculators are useful as long as they are used correctly and mistakes are avoided. Even so, you should always keep in mind that it might just be quicker and more reliable to work it out in your head or on paper.

Examples

Example 1

Use a calculator to evaluate 214+443.

Worked Solution
Create a strategy

Press the calculator buttons in order of the digits and symbols in the expression followed by the equals sign.

Apply the idea

Press the buttons: 2\, 1\,4\,+\,4\,4\,3\,= to get:214+443=657

Example 2

Using a calculator, evaluate 47-(14+(14\div7 )).

Worked Solution
Create a strategy

Press the calculator buttons in order of the digits and symbols in the expression followed by the equals sign.

Apply the idea

We can press the calculator buttons according this sequence: 4\,7\,-\,(\,1\,4\,+\,(\,1\,4\, \div \,7\,)\,)\,= to get: 47-(14+(14\div7 ))=31

Example 3

Xavier used his calculator to evaluate 16 \times 85 -2 and got the answer 926.

a

Is Xavier's answer correct?

Worked Solution
Create a strategy

Use a calculator to find the answer of the expression.

Apply the idea

Press the buttons: 1\,6\,\times \,8 \, 5 - \,2\,= to get the answer: 1358. So Xavier's answer is not correct.

b

What mistake might Xavier have made when he entered the expression into his calculator?

A
He swapped the digits in a number.
B
He added an extra zero.
C
He swapped some of the numbers.
D
He didn't use the correct order of operations.
Worked Solution
Create a strategy

Test the different options with your calculator until you manage to reproduce the wrong answer.

Apply the idea

Option A: He swapped the digits in a number. He either entered 61 \times 85 - 2 or 16 \times 58 - 2. Let's check using a calculator:

61 \times 85 - 2 = 5183

16 \times 58 - 2 = 926

The second one is the answer that Xavier got.

Option B: He added an extra zero. This cannot be what he did because he would have made the answer larger than 1358, but 926 \lt 1358.

Option C: He swapped some of the numbers. He either entered 85 \times 16 - 2 or 16 \times 2 - 85. Let's check using a calculator:

\begin{aligned} 85 \times 16 - 2 &= 1358 \\ 16 \times 2 - 85 &= -53 \end{aligned}

Option D: He didn't use the correct order of operations, so he performed the subtraction before the multiplication. Let's check using a calculator:

16\times(85 - 2) = 1328

Testing all the options, we have found out that Xavier swapped the digits in a number, so the correct answer is option A.

Idea summary

The buttons we need to use on our calculators are:

An image showing calculator buttons commonly used for operations. Ask your teacher for more information.

It's always useful to  check the reasonableness  of your answer. If the answer doesn't seem right, there's a good chance it isn't.

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